Question

Use complete sentences to analyze the graph of the function f(x) = log 1/3 x.

Part 1: Describe the domain, range, and general shape of this graph. (4 points)

Part 2: Using complete sentences, explain how plotting specific points helps graph the function and note any critical points such as its intercepts.

Answer 1

y = log (1/3) x
Part 1:
Domain : x ∈ ( 0, + ∞ ).
Range: y ∈ R.
General shape: The graph is decreasing.
Part 2 :
We will choose those points: x = { 1/3, 1, 3, 9 }
Ordered pairs ( for graphing the function ) are :
f ( x ) = { ( 1/3, 1 ), ( 1. 0 ), ( 3, - 1 ), ( 9, - 2 ) }.
There is no y - intercept and x - intercept is 1.